Inclusion Criteria:

          -  Pathologically (histologically or cytologically) proven (from primary lesion and/or
             lymph nodes) diagnosis of HPV-positive squamous cell carcinoma of the oropharynx,
             hypopharynx, or larynx; HPV-positivity will be defined as tumors that are p16-positive
             by immunohistochemistry

          -  Clinical stage III or IV disease; note: patients with M1 tumors are not eligible

          -  Appropriate stage for protocol entry, including no distant metastases, based upon the
             following minimum diagnostic workup:

               -  History/physical examination within 4 weeks prior to registration, including
                  assessment of weight loss in past 6 months

               -  Chest x-ray (or chest computed tomography [CT] scan or positron emission
                  tomography [PET]/CT scan) within 6 weeks prior to registration

          -  CT scan or magnetic resonance imaging (MRI) of the head and neck (of the primary tumor
             and neck nodes) and PET/CT scan

          -  Zubrod performance status 0-1

          -  Absolute neutrophil count (ANC) > 1,800 cells/mm^3

          -  Platelets > 100,000 cells/mm^3

          -  Hemoglobin (Hgb) > 8.0 g/dl (note: the use of transfusion or other intervention to
             achieve Hgb > 8.0 g/dl is acceptable)

          -  Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) < 2x the upper
             limit of normal

          -  Serum creatinine =< 1.5 mg/dl or institutional upper limit of normal

          -  Creatinine clearance (CC) >= 50 ml/min determined by 24-hour collection or estimated
             by Cockcroft-Gault formula

          -  Negative serum pregnancy test within 7 days prior to start of induction chemotherapy
             (ICT) for women of childbearing potential

          -  Women of childbearing potential and male participants are counseled on birth control
             and must agree to use a medically effective means of birth control throughout their
             participation in the treatment phase of the study (until at least 60 days following
             the last study treatment)

          -  Patient must sign study specific informed consent prior to study entry

        Exclusion Criteria:

          -  Prior invasive malignancy (except non-melanomatous skin cancer) unless disease free
             for a minimum of 3 years

          -  Patients with simultaneous primaries or bilateral tumors are excluded

          -  Patients who have had initial surgical treatment other than the diagnostic biopsy of
             the primary site or nodal sampling of the neck disease are excluded

          -  Patients with unknown primary tumor sites are excluded

          -  Patients who present with a cervical lymph node metastasis of unknown primary origin

          -  Prior systemic chemotherapy for the study cancer; note that prior chemotherapy for a
             different cancer is allowable

          -  Prior radiotherapy that would result in overlap of radiation therapy fields

          -  Primary site of tumor of oral cavity, nasopharynx, nasal cavity, paranasal sinuses, or
             salivary glands

          -  Recurrent head and neck cancer

          -  Current uncontrolled cardiac disease; i.e., uncontrolled hypertension, unstable
             angina, recent myocardial infarction (within prior 6 months), uncontrolled congestive
             heart failure, and cardiomyopathy with decreased ejection fraction

          -  Congestive heart failure with left ventricular ejection fraction < 20%

          -  Transmural myocardial infarction within the last 6 months

          -  Acute bacterial or fungal infection requiring intravenous antibiotics at registration

          -  Chronic obstructive pulmonary disease exacerbation or other respiratory illness
             requiring hospitalization or precluding study therapy at the time of registration

          -  Active lupus erythematosus or scleroderma with ongoing physical manifestations

          -  Any uncontrolled condition, which in the opinion of the investigator, would interfere
             in the safe and timely completion of study procedures

          -  Pregnant or lactating women or women of childbearing potential and men who are
             sexually active and not willing/able to use medically acceptable forms of
             contraception

          -  Prior allergic reaction to the study drug(s) involved in this protocol

          -  Patient is enrolled in another investigational trial